Continuous vs contiguous when talking about files

Continuous implies there is no discrete distinction between members, contiguous impies that the various members of the set are next to each other.

As an example, the visible spectrum of light is a continuous set, but when most people draw a rainbow, they put several colors right next to each other in a contiguous set.

Files are stored as discrete blocks on a drive, with the physical sectors lying one up against the other, but with discrete boundaries between each packet. Since each packet has a header, there is a discrete boundary, and as such, the correct word is contiguous.

Technically the word is contiguous.

That they happen to end up physically continuous is only an effect and not relevant.

An explanation: As you have already noted, fragmentation means parts of file are scattered across disk space. Joining these parts end to end will remove the space between the pieces, which is what causes loss of time.

contiguous means adjoining; without intervening space.

From Wikipedia:

In the maintenance of file systems, defragmentation is a process that reduces the amount of fragmentation. It does this by physically organizing the contents of the mass storage device used to store files into the smallest number of contiguous regions (fragments).

So you can use contiguous in the sense of adjacency.